Applied Functional Analysis

ISBN-13: 9781032476377 / Angielski / Miękka / 2023 / 632 str.

J. Tinsley Oden; Leszek Demkowicz

Opis

The textbook for Funcational Analysis provides not only solid mathematical foundations for the subject but, with many examples drawing from mechanics and science, motivates an engineering or science student to study the subject, and provides the necessary connections with applications. 

Applied Functional Analysis, Third Edition provides a solid mathematical foundation for the subject. It motivates students to study functional analysis by providing many contemporary applications and examples drawn from mechanics and science.

This well-received textbook starts with a thorough introduction to modern mathematics before continuing with detailed coverage of linear algebra, Lebesque measure and integration theory, plus topology with metric spaces.

The final two chapters provides readers with an in-depth look at the theory of Banach and Hilbert spaces before concluding with a brief introduction to Spectral Theory.

The Third Edition is more accessible and promotes interest and motivation among students to prepare them for studying the mathematical aspects of numerical analysis and the mathematical theory of finite elements.

Spis treści

Preliminaries

Elementary Logic and Set Theory

Relations; Functions

Cardinality of Sets

Foundations of Abstract Algebra

Elementary Topology in Rn

Elements of Differential and Integral Calculus

Linear Algebra

Vector Spaces—The Basic Concepts

Linear Transformations

Algebraic Duals; Euclidean Spaces

Lebesgue Measure and Integration

Lebesgue Measure

Lebesgue Integration Theory

Topological and Metric Spaces

Elementary Topology

Theory of Metric Spaces

Banach Spaces

Topological Vector Spaces

Hahn–Banach Extension Theorem

Bounded (Continuous) Linear Operators on Normed Spaces

Closed Operators

Topological Duals

Weak Compactness

Closed Range Theorem

Solvability of Linear Equations

Hilbert Spaces

Basic Theory

Duality in Hilbert Spaces

Elements of Spectral Theory

References

O autorze

J. Tinsley Oden is the Director of the Institute for Computational Engineering and Sciences (ICES) and Associate Vice President for

Research at The University of Texas at Austin. Dr. Oden is also a member of the US National Academy of Engineering and the

recipient of the 2009 SIAM Distinguished Career Award. He holds five honorary doctorates and was knighted Chevalier de l’Ordre

des Palmes Académiques by the French government.

Leszek F. Demkowicz is the Assistant Director of ICES and a professor in the Department of Aerospace Engineering and

Engineering Mechanics at The University of Texas at Austin. Dr. Demkowicz was one of the founding members of the Polish

Association for Computational Mechanics (PACM), serving as its first president from 1991 to 1993. His recent research has been

summarized in the two volumes Computing with hp-ADAPTIVE FINITE ELEMENTS (CRC Press, 2007 and 2008). For his work on

hp methods, he was awarded the 2009 Zienkiewicz Medal by PACM and the 2009 Computational and Applied Sciences Award by

the United States Association for Computational Mechanics (USACM).